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# 2.analysis of statically determinate structure

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### 2.analysis of statically determinate structure

1. 1. mhaviTüal½ysMNg;sIuvil viTüasßanCatiBhubec©keTskm<úCa @> karviPaKrcnasm<½n§kMNt;edaysþaTic Analysis of Statically Determinate Structures enAkñúgCMBUkenH eyIgnwgBiPakSaBITMrg;Fmμtarbs;eRKOgbgÁú<MEdlvisVkrRtUveFVIkarsikSaviPaK ehIyvak¾CaTMrg;EdlsßitenAkñúgbøg; ehIymüa:geTotRbB½n§kMlaMgGnuvtþn_k¾sßitenAelIbøg;eRKOgbgÁúMEdr. eyIgcab;epþImBiPakSaCamYynwgPaBcaM)ac;kñúgkareRCIserIsm:UEDlrbs;eRKOgbgÁúMd¾smRsbedIm,IeyIgGac kMNt;kMlaMgenAkñúgeRKOgbgÁúMeGaymantMélsuRkitEdlGacTTYlyk)an. bnÞab;mkeTot eyIgnwg BiPakSaBIlkçxNÐcaM)ac;sMrab;sßirPaBrbs;eRKOgbgÁúM. ehIycugeRkay mankarbgðajBIkarviPaKeRKOg bgÁúMsßitkñúgbøg;kMNt;edaysþaTicEdltP¢ab;edaytMN pin. @>!> m:UEDleRKOgbgÁúM (Idealized structure) Cak;Esþg eKminGacviPaKeRKOgbgÁúM)ansuRkiteT edaysareKRtUveFVIkar)a:n;RbmaNbnÞúk nigPaBFn;rbs;sMPar³. elIsBIenH eKRtUveFVIkarsnμt;BITItaMgEdlbnÞúkRtUveFVIGMeBIr. dUcenH va CakarsMxan;Nas;EdlvisVkrRtUvGPivDÆsmtßPaBkñúgkarbegáItm:UEDleRKOgbgÁúM. enAkñúgkfaxNÐ enHeyIgnwgENnaMBIbec©keTsCamUldæanEdlcaM)ac;sMrab;kargarenH. tMNTMr (Support Connection): Ggát;eRKOgbgÁúMRtUv)antamP¢ab;KñatamviFIeRcIn edayGaRs½yeTA elIectnarbs;visVkr. tMNsamBaØbIRbePTEdleKsÁal;PaKeRcInKW tMNsnøak; (pin connection)/ TMr rGil (roller support) nigtMNbgáb; (fixed joint). Pin-connection joint nig roller support GnuBaØat eGayGgát;vil)an Et fixed joint minGnuBaØateGayGgát;vileT ehIyCaTUeTAkareFVI fixed joint TamTar tMélx<s;. ]TahrN_éntMNTaMgenH ¬sMrab;Edk nigsMrab;ebtug¦RtUv)anbgðajenAkñúgrUbTI2-1 nig2-2 erogKña. tMNenAkñúgeRKOgbgÁúMeFVIGMeBIeQIPaKeRcInRtUv)aneKsnμt;faCa pin connection edaysarkar P¢ab;edayb‘ULúg nigedayEdkeKalminGacpþl;nUvkarTb;karvil (restraint) )anRKb;RKan;eT. Analysis of Statically Determinate Structures T.Chhay -24
2. 2. Department of Civil Engineering NPIC m:UEDleRKOgbgÁúMEdleRbIenAkñúgkarviPaKeRKOgbgÁúMEdltMNageGayTMrsnøak; (pinned support) nigTMrbgáb; (fixed support); nigtMNsnøak; (pin-connected joint) nigtMNbgáb; (fixed-connected joist) RtUv)anbgðajenAkñúgrUbTI 2-3 a nigrUbTI 2-3 b erogKña. EtkarBit RKb;tMNTaMgGs;manPaB rwgRkajxøHkñúgkarTb;Tl;nwgkarvil. sMrab;krNIEbbenH m:UEDlEdlsaksmCagsMrab;TMr b¤tMNRtUv )anbgðajenAkñúgrUbTI 2-3 c. RbsinebIefrkMrajTb;karrmYl (torsional spring constant) k = 0 eKKitfatMNCasnøak; ehIyRbsinebI k → ∞ eKKitfatMNCatMNbgáb;. enAeBleRCIserIsm:UEDlsMrab;TMr b¤tMNnImYy²rYcehIy visVkrRtUvdwgfakarsnμt;nwgCHT§iBl dl;kareFVIkarCak;Esþgrbs;Ggát; ehIyRtUvdwgfakarsnμt;enaHsmrmüsMrab;karsikSaKNnaeRKOgbgÁúM b¤Gt;. ]TarhN_ eKmanFñwmdUcbgðajenAkñúgrUbTI 2-4 a edayeKeRbIvaeGayRTbnÞúkcMcMnuc P . tMN EkgenARtg;cMnuc A dUckarbgðajenAkñúgrUbTI 2-1 a dUcenHeKGaceFVIm:UEDlTMrenHCaRbePTTMrsnøak; (pin support). elIsBIenH TMrRtg;cMnuc B RKan;EtTl;Ggát;kMueGayFøak; dUcenHeKeFVIm:UEDlvaCaTMrkl; (roller). kMras;rbs;FñwmRtUv)anecaledaysarvamanTMhMtUceFobnwgRbEvgrbs;Fñwm dUcenHm:UEDlrbs;FñwmRtUv)an karviPaKrcnasm<½n§kMNt;edaysþaTic T.Chhay -25
3. 3. mhaviTüal½ysMNg;sIuvil viTüasßanCatiBhubec©keTskm<úCa bgðajenAkñúgrUbTI 2-4 b. kardak;bnÞúkenAelIm:UEDlFñwmmanlkçN³RsedogKñanwgkardak;bnÞúkenAelI FñwmCak;Esþg. edIm,Ibgðajfam:UEDlenHmanlkçN³smRsb eyIgnwgBicarNakrNICak;lak;rbs;FñwmEdl eFVIBIEdkEdlmanRbEvg 6.1m nigrgbnÞúk P = 35.6m ehIysnμt;TMrenARtg;cMnuc A Ca TMrsnøak;. kar sikSaKNnaFñwmedayeRbI standard code procedures bgðajfa W 11× 22 mansmtßPaBRKb;RKan;kñúg karRTbnÞúkenH. edayeRbIviFIkMNt;PaBdabmYyenAkñúgCMBUk8 mMurgVil (rotation) enARtg;TMrsnøak;KW θ = 0.007rad = 0.40 o . BIrUbTI 2-4 c mMurgVilEbbenHeFVIeGaysøabxagelI nigsøabxageRkam pøas;TI )ancMgay Δ = θr = (0.0070rad )(127mm) = 0.889mm . tMNEdlmanbgðajenAkñúgrUbTI 2-1 a BitCa nwgpþl;nUvbrimaNd¾tUcEbbenHEmn dUcenHTMrsnøak;BitCasaksmsMrab;m:UEDlenH. RbePTtMNepSgeTotEdlEtgEtCYbRbTHenAelIeRKOgbgÁúMkñúgbøg;RtUv)anbgðajenAkñúgtarag 2- 1. vaBitCamansarsMxan;Nas;kñúgkarsÁal;nimitþsBaØa nigRbePTRbtikmμrbs;tMN b¤TMr. TMrGacbegáIt kMlaMgenAelIGgát;RbsinebIvaTb;Tl;nwgkarcl½trbs;Ggát; ehIyvanwgbegáItm:Um:g;RbsinebIvaTb;Tl;kar vilrbs;Ggát;. Ca]TahrN_ sMrab;Ggát;Edlb:HnwgépÞrelag (3) RtUv)ankarBarnwgkarcl½tEtmYyTis EdlEkgnwgépÞ. dUcenH épÞGnuvtþEdlkMlaMgEkg F eTAelIGgát;enAkñúgTisenaH. TMhMrbs;kMlaMgenH tMNageGaymYyGBaØat (unknown). ]TahrN_epSgeTot TMrbgáb; (fixed support) (7) karBarTaMgkar cl½t TaMgkarvilrbs;Ggát;enARtg;tMN. dUcenH TMrRbePTenHGnuvtþbgÁúMkMlaMgBIr nigm:Um:g;mYyeTAelI Ggát;. dUcenH sMrab;TMrbgáb;manGBaØatTaMgGs;cMnYnbI. Analysis of Statically Determinate Structures T.Chhay -26
4. 4. Department of Civil Engineering NPIC karviPaKrcnasm<½n§kMNt;edaysþaTic T.Chhay -27
5. 5. mhaviTüal½ysMNg;sIuvil viTüasßanCatiBhubec©keTskm<úCa enAkñúglkçN³Cak;Esþg TMrTaMgGs;GnuvtþkMlaMgBRgayelIépÞ (distributed surface load) eTAelI Ggát;Edlb:HnwgTMr. kMlaMgcMcMnuc (concentrated load) nigm:Um:g; (moment) EdlbgðajenAkñúgtarag 2-1 tMNageGaykMlaMgpÁÜbénkarBRgaybnÞúkTaMgenH. m:UEDleRKOgbgÁúM (Idealized structure): eday)anerobrab;BIviFIkñúgkarKitm:UEDléntMNenAelI eRKOgbgÁúM eyIgGacBiPakSaBIbec©keTskñúgkarbegáItm:UEDleRKOgbgÁúMsMrab;RbB½n§eRKOgbgÁúMepSg². dUc]TahrN_TImYy BicarNadgsÞÚc jib crane nig trolley enAkñúgrUbTI 2-5 a. sMrab;karviPaK eRKOgbgÁúMeyIgGacecalkMras;rbs;Ggát;emTaMgBIr ehIyeyIgsnμt;fatMNenARtg;cMnuc B CatMNrwg (rigid). elIsBIenH eKGaceFIVm:UEDltMNTMrenARtg;cMnuc A CaTMrbgáb; ehIykarlMGitBI trolley minRtUv )anKit. dUcenH Ggát;rbs;m:UEDleRKOgbgÁúMRtUv)ansMEdgedaybnÞat;BIrtP¢ab;Kña ehIybnÞúkenAelI hook RtUv)ansMEdgedaybnÞúkcMcMnuceTal F ¬rUbTI 2-5 b¦. CaerOy² eKeRbIFñwm nigr:tedIm,IRTkMralrbs;GKar. r:t (girder) CaGgát;emEdlRTbnÞúkrbs;kM- ral ÉGgát;muxkat;tUcCagEdlmanRbEvgElVgxøICag nigRtUv)antP¢ab;eTAnwgr:tRtUv)aneKeGayeQμaHfa Fñwm (beam). bnÞúkEdlmanGMeBImkelIFñwm b¤r:tCabnÞúkEdl)anBIkMralEdlFñwm b¤r:tRT. Ca]TahrN_ eKmaneRKagEdleRbIedIm,IRTkMralkMral ¬rUbTI 2-6 a¦. kMralenHRtUv)anRTeday floor joist ehIy Edl floor joist enHRtUv)anRTedayr:tBIr AB nig BC EdlenAsgxag. sMrab;karviPaKeKsnμt;fatMN CatMNsnøak; b¤tMNrGilEdltP¢ab;eTAnwgr:t ehIyr:tRtUv)anRTedayssrEdleKsnμt;faCaTMrsnøak; nig / b¤ TMrkl;. KMehIjBIxagelIrbs;RbB½n§eRKOgbgÁúMenHRtUv)anbgðajenAkñúgrUbTI 2-6 b. enAkñúgrUb enHbnÞat; EdltageGay joist minb:Hnwgr:t ehIybnÞat;EdltMNageGayr:tminb:Hnwgssr. karminb:H Analysis of Statically Determinate Structures T.Chhay -28
6. 6. Department of Civil Engineering NPIC enHtMNageGaytMNTMrsnøak; nig / b¤tMNTMrkl;. müa:gvijeTot RbsinebIeKcg;bgðajbøg;eRKagenHCa tMNbgáb; ¬eRbItMNpSarCMnYseGaytMNsamBaØedayb‘ULúg¦ enaHbnÞat;sMrab;Fñwm b¤r:tRtUvb:HnwgssrdUc enAkñúgrUbTI 2-7. dUcKña eKRtUvbgðaj Fixed-connected overhanging beam kñúgKMehIjBIelIdUcbgðaj enAkñúgrUbTI 2-8. RbsinebIkarsagsg;eRbIebtugGarem: Fñwm nigr:tRtUvtMNagedaybnÞat;Dub. CaTUeTA RbB½n§enH Ggát;TaMgGs;RtUvP¢ab;edaytMNbgáb; dUcenHeKKUrP¢ab;Ggát;eTAnwgTMr. ]TahrN_ rUbTI 2-9 a bgðajBIRkaPiceRKOgbgÁúMsMrab;RbB½n§ebtugGarem:Edlcak;enAnwgkEnøg (cast-in-place) ehIyrUbTI 2-9 b bgðajBIbøg;emIlBIelI. bnÞat;sMrab;FñwmCabnÞat;dac;edaysarvasßitenAeRkamkMral. karviPaKrcnasm<½n§kMNt;edaysþaTic T.Chhay -29
7. 7. mhaviTüal½ysMNg;sIuvil viTüasßanCatiBhubec©keTskm<úCa RkaPiceRKOgbgÁúM nigm:UEDleRKOgbgÁúMsMrab;rcnasm<½n§GMBIeQImanlkçN³RsedogKñanwgrcnasm<½n§ GMBIEdk. RbB½n§eRKOgbgÁúMEdlbgðajenAkñúgrUbTI 2-10 a bgðajBIsMNg; beam-wall ÉkMraldMbUl (roof deck) RtUv)anRTedayrnUteQI (wood joist) EdlbBa¢ÚnbnÞúkeTACBa¢aMgdæ. eKGacsnμt;farnUtRtUv)an RTedayTMrsamBaØenAelICBa¢aMg dUcenHeKGaceFVIm:UEDleRKOgbgÁúMdUcbgðajenAkñúgrUbTI 2-10 b. karepÞrbnÞúkBIépÞrgsMBaF (tributary loadings): enAeBlEdlépÞerobesμIdUcCaCBa¢aMg kMral b¤ dMbUlRtUv)anRTedayeRKag eKcaM)ac;RtUvkMNt;BIrebobénkarepÞrbnÞúkEdlmanGMeBIelIépÞenaHeTAGgát; eRKOgbgÁúMEdlRTva. CaTUeTA eKmanviFIBIrkñúgkarkMNt;va. kareRCIserIsviFIGaRs½ynwgragFrNImaRt rbs;RbB½n§eRKOgbgÁúM sMPar³EdlvaeFVI nigviFIkñúgkarsagsg;va. RbB½n§mYyTis (One-way system): karRTkMralEdlbBa¢ÚnbnÞúkeTAGgát;TMrtamskmμPaBmYyTis RtUv)aneKeGayeQμaHfa kMralxNÐmYyTis (one-way slab). edIm,IbgðajBIviFIénkarbBa¢ÚnbnÞúk cUrBi- carNaRbB½n§eRKagdUcbgðajenAkñúgrUbTI 2-11 a EdlFñwm AB / CD nig EF sßitenABIelIr:t AE nig BF . RbsinebIeKdak;bnÞúkrayesμI 4.8kN / m 2 enAelIkMral enaHeKsnμt;faFñwm CD RTbnÞúkEdlmanGMeBI enAelIépÞrgsMBaF (tributary area) AB EdlbgðajedayBN’ditenAelIbøg;eRKagbgÁúMenAkñúgrUbTI 2-11b. dUcenH Ggát; CD rgnUvkarBRgaybnÞúkefr (4.8kN / m 2 )(1.5m) = 7.2kN / m dUcbgðajenAelIm:UEDlFñwm enAkñúgrUbTI 2-11c. bnÞab;RbtikmμenAelIFñwmenH (10.8kN ) GnuvtþeTAelIr:t AE ¬nig BF ¦ cMkNþal dUcbgðajenAkñúgrUbTI 2-11d. edayeRbIviFIKMnitkñúgkarbBa¢ÚnbnÞúkEbbenH etIGñkmaneXIjcMENkrbs; kMralEdlenAsl;RtUv)anepÞreTAcugrbs;r:tKW 5.4kN b¤eT? Analysis of Statically Determinate Structures T.Chhay -30
8. 8. Department of Civil Engineering NPIC sMrab;RbB½n§kMralxøH eKtP¢ab;Fñwm nigr:teTAnwgssrenARtg;nIv:UdUcKña dUcbgðajenAkñúgrUbTI 2-12 a. RbsinebIeKCYbkrNIEbbenH eBlxøHeKk¾GacKitfakMralCakMralxNÐmYyTisEdr. ]TahrN_ Rbsin ebIkMralxNÐebtugGarem:EdlmanEdkBRgwgEtkñúgTismYy b¤eKcak;ebtugenAelIkMragEdlpñt; (corrugated metal deck) enaHeKsnμt;fabnÞúkRtUv)anbBa¢ÚntamskmμPaBmYyTis. müa:gvijeTot RbsinebIkMralCa kMralerobesμITaMgEpñkxagelI nigEpñkxageRkam ehIyRtUv)anBRgwgedayEdkkñúgTisTaMgBIr enaHeKKitfa bnÞúkRtUv)anbBa¢ÚneTAGgát;TMrtammYy Tis b¤tamBIrTis. ]TahrN_ eKmankMral nigbøg;eRKagdUcenAkñúg rUbTI 2-12b tamlkçxNÐTUeTA RbsinebI L2 ≥ L1 ehIyRbsinebIpleFobElVg (L2 / L1 ) ≥ 2 kMralxNÐ nwgeFVIkarCakMralxNÐmYyTis. edaysarEt L1 kan;EttUc Fñwm AB / CD nig EF pþl;nUvPaBrwgRkaj kan;EtFMkñúgkarRTbnÞúk. karviPaKrcnasm<½n§kMNt;edaysþaTic T.Chhay -31
9. 9. mhaviTüal½ysMNg;sIuvil viTüasßanCatiBhubec©keTskm<úCa RbB½n§BIrTis (Two-way system): RbsinebIpleFobElVgenAkñúgrUbTI 2-12 b KW (L 2 / L1 ) < 2 eKsnμt;fabnÞúkRtUv)anbBa¢ÚneTAFñwm nigr:ttamskmμPaBBIrTis. sMrab;kMralEdlCYbkrNIEbbenH RtUv )aneKeGayeQμaHfa kMralxNÐBIrTis (two-way slab). edIm,IbgðajBIviFIkñúgkaredaHRsaykrNIenH cUr BicarNakMralebtugGarem:ragkaerenAkñúgrUbTI 2-13 a EdlRTedayFñwmxagcMnUnbYn AB / BD / DC nig DC EdlmanRbEvg 3m . enATIenH L2 / L1 = 1 . edaysarkMralxNÐrgskmμPaBBIrTis épÞrgsMBaF sMrab;Fñwm AB RtUv)anbgðajedayBN’ditenAkñúgrUbTI 2-13b. épÞenHRtUv)ankMNt;edaybnÞat;Ggát; RTUg 45o dUcbgðaj. dUcenH RbsinebIbnÞúkrayesμI 4.8kN / m 2 GnuvtþenAelIkMral GaMgtg;sIuetrbs;bnÞúk EdlGnuvtþenARtg;cMnuckNþalFñwmKW (4.8kN / m 2 )(1.5m) = 7.2kN / m ehIybnÞúkEdlBRgayenAelIFñwm enHmanragRtIekaNdUcbgðajenAkñúgrUbTI 2-13c. sMrab;]ThrN_enAkñúgkrNI L2 / L1 = 1.5 eKcaM)ac; sg;bnÞat; 45o dUcbgðajenAkñúgrUbTI 2-14a. bnÞúk 4.8kN / m 2 EdlGnuvtþenAelIkMralnwgbegáItbnÞúk BRgayragctuekaNBñay nigragRtIekaNenAelIGgát; AB nig AC dUcbgðajenAkñúgrUbTI 2-14b nig2- 14c erogKña. Analysis of Statically Determinate Structures T.Chhay -32
10. 10. Department of Civil Engineering NPIC ]TahrN_2-1³ kMralrbs;fñak;eronmYyRtUv)anRTedayrnUtr)ar (bar joist) dUcbgðajenAkñúgrUbTI 2- 15 a. rnUtnImYy²manRbEvg 4.5m ehIyvamanKMlatBIKña 0.75m KitBIG½kS. kMralenHRtUv)ansagsg;BI ebtugTMgn;RsalEdlmankMras;100mm . edayminKitTMgn;pÞal;rbs;rnUt nigkMralEdkpñt; (corrugated metal deck) cUrkMNt;bnÞúkEdlmanGMeBIenAelIrnUtnImYy². dMeNaHRsay³ bnÞúkefrenAelIkMralKWbNþalBITMgn;rbs;kMralebtug. BItarag 1-3 TMgn;ebtugTMgn;RsalkMras; 100mm KW (100)(0.015kN / m 2 ) = 1.50kN / m 2 . BItarag1-4 bnÞúkGefrsMrab;fñak;eronKW1.92kN / m 2 . dUcenH bnÞúkkMralsMrubKW1.50klN / m 2 + 1.92kN / m 2 = 3.42kN / m 2 . sMrab;RbB½n§kMral L1 = 0.75m nig L2 = 4.5 . edaysar L2 / L1 > 2 eKKitkMralxNÐCakMralxNÐmYyTis. épÞrgsMBaFsMrab;rnUtnImYy² RtUv)anbgðajenAkñúgrUbTI 2-15 b. dUcenH bnÞúkrayesμIenArnUtKW w = 3.42kN / m 2 (0.75m ) = 2.57 kN / m bnÞúk nigRbtikmμenAelIGgát;rnUtnImYy²RtUv)anbgðajenAkñúgrUbTI 2-15c. ]TahrN_2-2³ kMraldMbUlrabesμIénGKareRKagEdkenAkñúgrUbTI 2-16a RtUv)aneKeRbIedIm,IRTbnÞúk srub 2kN / m 2 EdlmanGMeBIelIépÞkMral. RbsinebIFñwm AD nig BC manRbEvg 5m ehIymanKMlat 3m ¬Fñwm AB nig DC ¦. cUrkMNt;bnÞúkdMbUl (roof load) enAkñúgtMbn; ABCD EdlRtUv)anbBa¢ÚneTAFñwm BC . karviPaKrcnasm<½n§kMNt;edaysþaTic T.Chhay -33
11. 11. mhaviTüal½ysMNg;sIuvil viTüasßanCatiBhubec©keTskm<úCa dMeNaHRsay³ enAkñúgkrNIenH L1 = 5m ehIy L2 = 3m . edaysar L2 / L1 < 2 enaHkMralxNÐeFVIkartamBIrTis. bnÞúkenAelIépÞrgsMBaFRtUv)anbgðajenAkñúgrUbTI 2-16b EdlépÞctuekaNBñayénbnÞúkEdlmanBN’dit RtUv)anbBa¢ÚneTAGgát; BC . GaMgtg;sIuetrbs;bnÞúkenARtg;kMBUlKW (2kN / m 2 )(1.5m) = 3kN / m . Ca lT§pl karBRgaybnÞúkenAelIGgát; BC RtUv)anbgðajenAkñúgrUbTI 2-16b. eKk¾KYreFVIkarKNnakar bBa¢únbnÞúkenAelIépÞrgsMBaFsMrab;tMbn;kaerBIrEdlenAxagsþaMrbs;Ggát; BC enAkñúgrUbTI 2-16a ehIy bnÞúkEdl)anKNnabEnßmenHk¾RtUv)andak;enAelIGgát; BC Edr. @>@> eKalkarN_tMrYtpl (Principle of superposition) eKalkarN_tMrYtplbegáItnUvmUldæansMrab;RTwsþIviPaKeRKOgbgÁúM (theory of structural) CaeRcIn. eKalkarN_BN’nafa³ eKGackMNt;bMlas;TIsrub b¤kMlaMgxagkñúg (internal loading or force) srubenA Rtg;cMnucNamYyenAelIeRKOgbgÁúMEdlrgbnÞúkxageRkACaeRcInedaykarbUkbMlas;TI b¤kMlaMgxagkñúgEdl bNþalBIbnÞúkxageRkAnImYy²bBa©ÚlKña. edIm,IGnuvtþeKalkarN_tMrYtplenH)an bnÞúk kugRtaMg nigbM- las;TIRtUvEtCalIenEGr (linear). edIm,IGnuvtþeKalkarN_pl eKRtUvbMeBjtMrUvkarcMnYnBIrxaeRkam³ sMPar³RtUvEteFVIkarenAkñúgTMrg;lIenEGreGLasÞic (linear-elastic) dUcenHmann½yfaeKGac eRbIc,ab;h‘Uk (Hook’s law) )an ehIybnÞúksmamaRteTAnwgbMlas;TI. Analysis of Statically Determinate Structures T.Chhay -34
12. 12. Department of Civil Engineering NPIC ragFrNImaRtrbs;eRKOgbgÁúMminRtUvrgkarERbRbYlFMeRkamGMeBIrbs;bnÞúkeT mann½yfaeK GnuvtþRTwsþIbMlas;TItUc (small displacement theory). bMlas;TIFMnwgpøas;bþÚrTItaMg nig Tisrbs;bnÞúky:agxøaMg. ]TahrN_ r)arEdkkugs‘ulesþIgEdlrgkMlaMgenAxagcugrbs;va. enAkñúgesovePAenH BN’naEtBIsMPar³lIenEGreGLasÞic ehIybMlas;TIEdlekItedaysabnÞúk minpøas;bþÚrTisedArbs;bnÞúkGnuvtþn_FM ehIyk¾minpøas;bþÚrTMhMEdleRbIsMrab;KNnam:Um:g;énkMlaMgFMEdr dUcenHtMrUvkarTaMgxagelIRtUv)anbMeBj. @>#> smIkarlMnwg (Equation of equilibrium) enAkñúgsþaTic)anEcgfa eRKOgbgÁúM b¤Ggát;mYyéneRKOgbgÁúMmanlMnwg enAeBlNaEdlvaGacrkSa lMnwgénkMlaMg niglMnwgénm:Um:g;. CaTUeTA eKRtUvbMeBjnUvlMnwgénsmIkarkMlaMg nigsmIkarm:Um:g;tam G½kSTaMgbI mann½yfa³ ∑ Fx = 0 ∑ Fy = 0 ∑ Fz = 0 ∑Mx = 0 ∑M y = 0 ∑Mz = 0 (2-1) b:uEnþ PaKeRcIneRKOgbgÁúMeRcInRTcMENkbnÞúkEdlsßitenAkñúgbøg;eTal ehIyedaysarEtbnÞúkk¾sßitenAkñúg bøg;enaH smIkartMrUvkarxagelIkat;bnßymkRtwm ∑ Fx = 0 ∑ Fy = 0 ∑ MO = 0 (2-2) enATIenH ∑ Fx nig ∑ Fy CaplbUkBiCKNiténbgÁúMkMlaMgtamG½kS x nigtamG½kS y erogKña EdlmanGMeBI mkelIeRKOgbgÁúM b¤Ggát;mYyrbs;eRKOgbgÁúM ehIy ∑ M O CaplbUkBiCKNiténm:Um:g;énkMlaMgCMuvijG½kS EdlEkgnwgbøg; x − y ¬G½kS z ¦ ehIykat;tamcMnuc O . enARKb;eBlEdleKGnuvtþsmIkarTaMgenH dMbUgeKcaM)ac;RtUvKUrdüaRkamGgÁesrI (free body diagram) rbs;eRKOgbgÁúM b¤rbs;Ggát;. edIm,IKUrdüaRkamGgÁesrI eKRtUvpþac;Ggát;ecjBIKña nigecjBITMr. kMlaMgxageRkA kMlaMgkñúg b¤kMlaMgRbtikmμRtUvbgðajenAelIGgát;Edl)anpþac;ecj. tamry³enH eKGac kMNt;kMlaMgRbtikmμenARtg;TMredayeRbItarag 2-1. ehIyeyIgRtUvcaMpgEdrfa enAelIdüaRkamGgÁesrI kMlaMgkñúgénGgát;BIrEdlP¢ab;KñamanTMhMdUcKña EtmanTispÞúyKña. RbsinebIeKcg;kMNt;kMlaMgkñúgenARtg;cMnucCak;lak;enAkñúgGgát; eKRtUveRbIviFImuxkat; (method of section). viFIenHtMrUveGaykat;Ggát;tamTisEkgeTAnwgG½kSrbs;Ggát;Rtg;cMnucEdleKRtUvkarkMNt; kMlaMgkñúg. eKRtUvKUrdüaRkamGgÁesrIénkMNat;Ggát;nImYy²Edl)ankat; rYckMNt;kMlaMgkñúgedayGnuvtþ smIkarlMnwgeTAelIkMNat;Ggát;enaH. CaTUeTA kMlaMgkñúgEdlmanGMeBIenAelImuxkat;rbs;Ggát;Edlkat; rYmmankMlaMgEkg (normal force) N / kMlaMgkat; (shear force) V nigm:Um:g;Bt; (bending moment) karviPaKrcnasm<½n§kMNt;edaysþaTic T.Chhay -35
13. 13. mhaviTüal½ysMNg;sIuvil viTüasßanCatiBhubec©keTskm<úCa M dUcbgðajenAkñúgrUbTI 2-17. eyIgnwgBiBN’naeKalkarN_sþaTicEdleRbIedIm,IkMNt;RbtikmμxageRkAenAelIeRKOgbgÁúMenAkñúg kfaxNÐ 2.5. eyIgnwgBiPakSaBIkMlaMgkñúgenAkñgGgát;eRKOgbgÁúMenAkñúgCMBUkTI 4. ú @>\$> PaBkMNt; nigsßirPaB (Determinacy and stability) muxnwgcab;epþImviPaKkMlaMgrbs;eRKOgbgÁúM eKcaM)ac;kMNt;nUvPaBkMNt; nigsßirPaBrbs;eRKOgbgÁúM. PaBkMNt; (determinacy): smIkarlMnwgpþl;nUvlkçxNÐcaM)ac; nigRKb;RKan;sMrab;lMnwg. enAeBl EdlRKb;kMlaMgTaMgGs;enAkñúgeRKOgbgÁúMGackMNt;edayeRbIsmIkarlMnwgxagelI enaHeKehAeRKOgbgÁúM enaHCa eRKOgbgÁúMkMNt;edaysþaTic (statically determinate structure). sMrab;eRKOgbgÁúMEdlmancMnYn kMlaMgCaGBaØateRcInCagcMnYnsmIkarEdlGacman eKeGayeQμaHvafa eRKOgbgÁúMminkMNt;edaysþaTic (statically indeterminate structure). tamc,ab;TUeTA eKGackMNt;faeRKOgbgÁúMmYyCaeRKOgbgÁúMkMNt; edaysþaTic b¤k¾eRKOgbgÁúMminkMNt;edaysþaTicedayKUrdüaRkamGgÁesrIénGgát;TaMgGs;rbs;va b¤épñkén Ggát;EdleRCIserIs ehIybnÞab;mkeRbobeFobcMnYnGBaØatsrubEdlCakMlaMg nigm:Um:g;CamYynwgcMnYn srubénsmIkarlMnwgEdlGacman*. sMrab;eRKOgbgÁúMkñúgbøg; eKmansmIkarlMnwgbIsMrab;Ggát;nImYy² dUcenHRb sinebIeKmanGgát;srubcMnYn n ehIykMlaMgRbtikmμ nigm:Um:g;RbtikmμcMnYn r enaHeyIg)an r = 3n / kMNt;edaysþaTic r > 3n / minkMNt;edaysþaTic (2-3) CaebIvaCaeRKOgbgÁúMminkMNt;edaysþaTic enaHeKRtUvkarsmIkarbEnßmedIm,IedaHRsayrkRbtikmμEdlCaGBaØatedayP¢ab;TMnak;TMngrvagbnÞúkGnuvtþ n_ nigRbtikmμeTAnwgbMlas;TI b¤mMurgVilenARtg;cMnucepSgKñaenAelIRKOgbgÁúM. smIkarTaMgenHCasmIkarRtUv Kña (compatibility equation) ehIyvaRtUvmancMnYnesμInwgdWeRkénPaBminkMNt;rbs;eRKOgbgÁúM. smIkar compatibility Tak;TgnwglkçN³FrNImaRt niglkçN³rUbrbs;eRKOgbgÁúM ehIyeyIgnwgelIkykvamk * karKUrdüaRkamGgÁesrImincaM)ac;CaTUeTAeT edaysareKGacrab;cMnUnGBaØat ehIyeFVIkareRbobeFobCamYynwgcMnUnsmIkar lMnwg)an. Analysis of Statically Determinate Structures T.Chhay -36
14. 14. Department of Civil Engineering NPIC BN’naenAkñúgCMBUkTI 10. ]TahrN_ 2>3³ cat;cMNat;fñak;rbs;FñwmnImYy²EdlbgðajenAkñúgrUbTI 2-18 a rhUtdl; 2-18 d Ca eRKOgbgÁúMkMNt;edaysþaTic b¤eRKOgbgÁúMminkMNt;edaysþaTic. eKsnμt;faeKsÁal;kMlaMgEdlGnuvtþmin elIFñwm ehIyvaGacmanGMeBIenARKb;TItaMgTaMgGs;rbs;Fñwm. dMeNaHRsay³ eKRtUvpþac;FñwmpSM (compound beam) enAkñúgrUbTI 2-18c nig 2-18d EdlpSMeLIgGgát;EdltP¢ab;Kña edaytMNsnøak;ecjBIKña. cMNaMfa enAkñúgkrNITaMgenH kMlaMgRbtikmμEdlCaGBaØatEdlmanGMeBIenA cenøaH Ggát;nImYy²RtUv)anbgðajCaKU EtmanTispÞúyKña. düRkamGgÁesrIRtUv)anbgðaj. edayGnuvtþ r = 3n b¤ r > 3n lT§plénkarcat;cMNat;fñak;RtUv)anbgðaj. ]TahrN_ 2>4³ cat;cMNat;fñak;rbs;eRKOgbgÁúMEdltP¢ab;edaytMNsnøak;EdlbgðajenAkñúgrUbTI 2-19 a rhUtdl; 2-19 d CaeRKOgbgÁúMkMNt;edaysþaTic b¤CaeRKOgbgÁúMminkMNt;edaysþaTic. RbsinebIvaCa eRKOgbgÁúMminkMNt;edaysþaTic cUrR)ab;BIcMnYnéndWeRkénPaBminkMNt;. eRKOgbgÁúMrgnUvbnÞúkxageRkAEdl karviPaKrcnasm<½n§kMNt;edaysþaTic T.Chhay -37
15. 15. mhaviTüal½ysMNg;sIuvil viTüasßanCatiBhubec©keTskm<úCa eKsnμt;sÁal; ehIyvamanGMeBIenARKb;TItaMgTaMgGs;rbs;eRKOgbgÁúM. dMeNaHRsay³ karcat;cMNat;fñak;én;eRKOgbgÁúMEdltP¢ab;edaytMNsnøak;manlkçN³RsedogKñanwgFñwmEdr. düRkamGgÁ esrIRtUv)anbgðaj. edayGnuvtþ r = 3n b¤ r > 3n lT§plénkarcat;cMNat;fñak;RtUv)anbgðaj. ]TahrN_ 2>5³ cat;cMNat;fñak;rbs;eRKagEdlbgðajenAkñúgrUbTI 2-20a nig2-20d CaeRKOgbgÁúM kMNt;edaysþaTic b¤CaeRKOgbgÁúMminkMNt;edaysþaTic. RbsinebIvaCa eRKOgbgÁúMminkMNt;edaysþaTic cUrR)ab;BIcMnYnéndWeRkénPaBminkMNt;. eRKOgbgÁúMrgnUvbnÞúkxageRkAEdl eKsnμt;sÁal; ehIyvaman GMeBIenARKb;TItaMgTaMgGs;rbs;eRKOgbgÁúM. dMeNaHRsay³ karkMNt;sßirPaB nigPaBkMNt;rbs;eRKOgbgÁúMeRKagmindUcKñanwgkarkMNt;sMrab;Fñwm nigeRKOgbgÁúMEdlt Analysis of Statically Determinate Structures T.Chhay -38
16. 16. Department of Civil Engineering NPIC P¢ab;edaytMNsnøak;eT eRBaHeRKagpSMeLIgedayGgát;EdltP¢ab;Kñaedaysnøak;rwg. eBlxøHGgát;begáIt tMbn;biTCitxagkñúg dUcenAkñúgrUbTI 2-20a. enATIenH ABCD begáIttMbn;biTCit. edIm,Icat;cMNat;fñak; rbs;eRKOgbgÁúMTaMgenH eKcaM)ac;RtUveRbIviFImuxkat; ehIykat;EpñkEdlbiTCit. eRkayeBleKKUrdüaRkam GgÁesrIrbs;EpñkEdlkat;rYcehIy enaHeKGaccat;cMNat;fñak;rbs;eRKag)an. cMNaMfa eKRtUvkarEtEpñk mYyrbs;muxkat;Edlkat;tamtMbn;biTCit. enAeBlEdleKkMNt;GBaØatenARtg;muxkat;rYcehIy eKGac kMNt;kMlaMgkñúgenARKb;cMnucTaMgGs;enAkñúgGgát;edayeRbIviFImuxkat; nigsmIkarlMnwg. eRKagenAkñúgrUbTI 2-20b manmintMbn;biTCit dUcenHedIm,IrkPaBkMBt;vaminRtUvkarkarkat;cenøaHTMreT. lT§plénkarcat; cMNat;fñak;RtUv)anbgðajenAkñúgrUbTI 2-20a nig 2-20b. sßirPaB (stability): edIm,IFananUvsßanPaBlMnwgrbs;eRKOgbgÁúM nigGgát;rbs;va eKminRtwmEtbMeBj smIkarlMnwgb:uENÑaHeT b:uEnþGgát;RtUvEtTb; (constraint) y:agl¥ nigRtwmRtUvedayTMrrbs;va. sßanPaB BIrnwgekItmaneLIgenAeBlNaEdlTMrmin)anTb;RtwmRtUv. karTb;mineBjelj (partial constraints): enAkñúgkrNIxøH eRKOgbgÁúM b¤Ggát;rbs;vaGacman kMlaMgRbtikmμticCagsmIkarlMnwgEdlRtUvbMeBj eBlenaHeRKOgbgÁúMnwgkøayCaeRKOgbgÁúMEdlTb;mineBj elj (partially constrained structure). ]TahrN_ eKmanGgát;EdlbgðajenAkñúgrUbTI 2-21 CamYy nwgdüaRkamGgÁesrIrbs;va. enATIenHsmIkar ∑ Fx = 0 minRtUv)anbMeBjsMrab;lkçxNÐdak;bnÞúk dUcenH Ggát;KμansßirPaB. karviPaKrcnasm<½n§kMNt;edaysþaTic T.Chhay -39
17. 17. mhaviTüal½ysMNg;sIuvil viTüasßanCatiBhubec©keTskm<úCa karTb;minRtwmRtUv (improper constraints): enAkñúgkrNIxøHEdlcMnYnénkMlaMgEdlCaGBaØat nig cMnYnénsmIkarlMnwgesμIKña b:uEnþvaenAEtGaceFIVeGayeRKOgbgÁúMcl½t)an b¤KμansßirPaB edaysarEtkarTb; minRtwmRtUvrbs;TMr. krNIEbbenHekItmanenAeBlEdlExSskmμénkMlaMgRbtikmμrbs;TMrkat;KñaRtg;cMnuc mYy. ]TahrN_sMrab;krNIRtUv)anbgðajenAkñúgrUbTI 2-22. BIdüaRkamGgÁesrIrbs;Fñwm eyIgeXIjfa plbUkm:Um:g;Rtg;cMnuc O nwgminesμIsUnüeT ¬ Pd ≠ 0 ¦ dUcenHvanwgekItmankarvilCuMvijcMnuc O . Analysis of Statically Determinate Structures T.Chhay -40
18. 18. Department of Civil Engineering NPIC viFImü:ageTotEdlkarTb;minRtwmRtUvrbs;TMrnaMeGaymaneRKOgbgÁúMKμansßirPaBekItmanenAeBl EdlkMlaMgRbtikmμTaMgGs;manTisRsbKña. ]TahrN_sMrab;krNIRtUv)anbgðajenAkñúgrUbTI 2-23. enA eBlEdleKGnuvtþkMlaMgeRTt P plbUkkMlaMgtamTisedknwgminesμIsUnüeT. CaTUeTA eRKOgbgÁúMnwgKμansßirPaBedaylkçN³FrNImaRt ¬rMkiltictYc b¤dYlrlM¦ RbsinebIva mankMlaMgRbtikmμticCagsmIkarlMnwg b¤RsinebIvamankMlaMgRbtikmμRKb;RKan; EtGsßirPaBrbs;nwgekIt manRbsinebIExSskmμénkMlaMgRbtikmμkat;KñaRtg;cMnucmYy b¤k¾RsbKña. RbsinebIeRKOgbgÁúMpSMeLIgeday Ggát;eRcIn eKGackMNt;GsßirPaBrbs;Ggát;mYy b¤rbs;Ggát;eRcInedaykarGegát. RbsinebIGgát;begáIt collapsible mechanism )an eRKOgbgÁúMnwgminmansßirPaB. eyIgGackMNt;sßirPaBtamrUbmnþ)ansMrab; eRKOgbgÁúMkñúgbøg;Edlman n nigGBaØatEdlCakMlaMgRbtikmμ r ehIyedaysarGgát;nImYy²RtUvman smIkarlMnwgcMnYnbI enaH r < 3n KμansßirPaB r ≥ 3n KμansßirPaBenAeBlEdlkMlaMgRbtikmμrbs;Ggát; kat;KñaRtg;cMnucmYy b¤RsbKña b¤Ggát;xøHbegáIt collapse mechanism (2-4) eKRtUveCosvaRbePTeRKOgbgÁúMEdlKμansßirPaBeTaHbICavaCaeRKOgbgÁúMkMNt;edaysþaTic b¤eRKOg bgÁúMminkMNt;edaysþaTick¾eday. ]TahrN_ 2>6³ cUrcat;cMNat;fñak;rbs;eRKOgbgÁúMnImYy²enAkñúgrUbTI 2-24a rhUtdl;2-24e CaeRKOg bgÁúMmansßirPaB b¤KμansßirPaB. eRKOgbgÁúMrgnUvbnÞúkxageRkANamYyEdleyIgsnμt;vasÁal;. dMeNaHRsay³ eRKOgbgÁúMRtUv)ancat;cMNat;fñak;dUcbgðajkñúgrUb. karviPaKrcnasm<½n§kMNt;edaysþaTic T.Chhay -41
19. 19. mhaviTüal½ysMNg;sIuvil viTüasßanCatiBhubec©keTskm<úCa Analysis of Statically Determinate Structures T.Chhay -42
20. 20. Department of Civil Engineering NPIC @>%> karGnuvtþénsmIkarlMnwg (Application of the equation of equilibrium) eBlxøH Ggát;rbs;eRKOgbgÁúMRtUv)antP¢ab;KñaedaytMNEdleKsnμt;faCatMNsnøak;. eRKagGKar nig truss CaRbePTeRKOgbgÁúMEdlCaerOy²sagsg;edayeRbItMNEbbenH. kñúgkrNIeRKOgbgÁúMkñúgbøg; EdltP¢ab;edaysnøak;mankarTb;RtwmRtUv nigminmanTMrelIs b¤Ggát;elIsedIm,IkarBarkardYlrlM enaHeK GackMlaMgEdlmanGMeBIenARtg;tMN nigenARtg;TMredayGnuvtþsmIkarlMnwgTaMgbI ¬ ∑ Fx = 0 / ∑ Fy = 0 ∑ M O = 0 ¦ eTAelIGgát;nImYy². enAeBlEdleKTTYl)ankMlaMgenARtg;tMN eKGacsikSaKNaTMhM rbs;Ggát; kartP¢ab; nigTMredayEp¥kelI design code specification. edIm,IbgðajBIviFIénkarviPaKkMlaMg BicarNaeRKagEdlmanGgát;bIdUcbgðajenAkñúgrUbTI 2-25a EdlrgnUvbnÞúk P1 nig P2 . düaRkamGgÁesrIrbs;Ggát;nImYy²RtUv)anbgðajenAkñúgrUbTI 2-25b. Ca srub eKmanGBaØatTaMgGs; 9 ehIyeKmansmIkarlMnwgTaMgGs; 9 EdlGgát;nImYy²mansmIkarlMnwg 3 dUcenHeRKOgbgÁúMenHCaeRKOgbgÁúMkMNt;edaysþaTic. sMrab;dMeNaHRsayCak;Esþg ¬eBlxøHmanlkçN³ gayRsYl¦ eKGacBicarNaeRKagCaEpñk b¤k¾eRKagTaMgmUl enAeBlEdlGnuvtþsmIkarxøHénsmIkarTaMg 9 enH. Ca]TahrN_ düaRkamGgÁesrIéneRKagTaMgmUlRtUv)anbgðajenAkñúgrUbTI 2-25c. eKGackMNt; kMlaMgRbtikmμTaMgbI Ax / Ay nig C x enAelIRbB½n§eRKOgbgÁúMEdltP¢ab;edaytMNsnøak;rwgraMenH bnÞab;mk viPaKGgát;BIrkñúgcMeNamGgát;TaMgGs;enAkñúgrUbTI 2-25b edIm,ITTYl)anGBaØat 6 epSgeTot. elIsBI enH eKGacRtYtBinitücMeLIyCaEpñkedayGnuvtþsmIkarlMnwgTaMgbIeTAelIGgát;TIbIEdlenAsl;. Casegçb eKGacedaHRsaybBaðaenHedaysresrsmIkarlMnwgy:ageRcInNas;cMnYn 9 edayeRbIdüaRkamGgÁesrIén Ggát;nImYy² nig / b¤bnSMénGgát;EdltP¢ab;. smIkareRkABIsmIkarTaMg 9 xagelIRtUv)aneRbIedIm,IRtYt BinitülT§pl. karviPaKrcnasm<½n§kMNt;edaysþaTic T.Chhay -43
21. 21. mhaviTüal½ysMNg;sIuvil viTüasßanCatiBhubec©keTskm<úCa LÚvBicarNaeRKagEdlmanGgát;BIrdUcbgðajenAkñúgrUbTI 2-26a . enATIenHdüaRkamGgÁesrI rbs;Ggát;bgðajGBaØatcMnYn 6 ¬rUbTI 2-26b¦ ehIyeyIgGacsresrsmIkarlMnwgcMnYn 6 EdlGgát; nImYy²mansmIkarlMnwgcMnYn 3 dUcenHvaCaeRKOgbgÁúMkMNt;edaysþaTic. dUckñúgkrNIelIkmun eKk¾Gac eRbIdüaRkamGgÁesrIrbs;eRKOgbgÁúMTaMgmUl ¬rUbTI 2-26c¦ edIm,IviPaKpgEdr. dUcbgðajenAkñúgrUb eRKagnwgdYlrlMRbsinebIKμanTMr edayvanwgvilCMuvijsnøak; B EtkrNIenHnwgminekItmaneT edaysar RbB½n§kMlaMgEdlmanGMeBIenAelIeRKagTaMgGs;eFVIeGayeRKagmanlMnwg. dUcenH eKGacKNnaGBaØatTaMg 6 enHedayGnuvtþsmIkarlMnwgTaMgbIeTAelIeRKagTaMgmUl ¬rUbTI 2-26c¦ ehIydUcKñaGnuvtþsmIkarTaMg bIeTAelIGgát;mYykñúgcMeNamGgát;TaMgBIr. ]TahrN_TaMgBIrxagelIbgðajfa RbsinebIeRKagRtUv)anRTedayTMrd¾RtwmRtUv nigminmanTMr b¤ Ggát;caM)ac;eRcInCagenHedIm,IkarBarkardYlrlM enaHeRKagCaeRKagkMNt;edaysþaTic ehIyeKGackMNt; GBaØatEdlCakMlaMgenARtg;TMr nigtMNBIsmIkarlMnwgedayGnuvtþeTAelIGgát;nImYy². ehIyRbsinebI eRKOgbgÁúMenAEtrwgmaM ¬minGacdYlrlM¦ enAeBleKdkTMrecj ¬rUbTI 2-25c¦ enaHeKGackMNt;Rbtikmμ TMrTaMgbIedayGnuvtþsmIkarlMnwgeTAelIeRKOgbgÁúMTaMgmUl. b:uEnþRbsinebIeRKOgbgÁúMbgðajPaBminrwgmaM ¬GacdYlrlM¦ bnÞab;BIeKdkTMrecj ¬rUbTI 2-26c¦ enaHeKRtUvpþac;Ggát;TaMgenaHecjBIKña ehIyeKRtUv BicarNalMnwgrbs;Ggát;nImYy²edIm,ITTYl)ansmIkarRKb;RKan;edIm,IkMNt;RbtikmμTMrTaMgGs;. Analysis of Statically Determinate Structures T.Chhay -44
22. 22. Department of Civil Engineering NPIC dMeNIrkarkñúgkarviPaK (Procedure for analysis) CMhanxageRkampþl;nUvviFIsMrab;kMNt;kMlaMgRbtikmμsMrab;eRKOgbgÁúMEdlpSMedayGgát;EdltP¢ab; edaytMNsnøak;. düaRkamGgÁesrI (Free-body diagrams) pþac;rcnasm½<n§ nigKUrdüaRkamGgÁesrIénGgát;nImYy². ehIy vanwgkan;EtgayRsYl Rbsin ebIeyIgKUrdüaRkamGgÁesrIrbs;eRKOgbgÁúMTaMgmUlbEnßmBIelIdüaRkamGgÁesrIrbs;Ggát;nI- mYy². eKGackMNt;RbtikmμTMrxøH b¤TaMgGs;edayeRbIdüaRkamenH. eyIgRtUvcgcaMfakMlaMgRbtikmμrbs;Ggát;BIreFVIGMeBICamYynwgTMhMesμIKña b:uEnþmanTisedApÞúy KñaenAelIdüaRkamGgÁesrIrbs;Ggát;. enAkñúgkrNIxøH eyIgGacdwgBITisedArbs;kMlaMgEdlCaGBaØat b:uEnþRbsinebIeyIgBi)akkñúg karkMNt;TisedArbs;va eyIgGacsnμt;)an. smIkarlMnwg (Equation of equilibrium) rab;cMnYnGBaØatsrubedIm,IeGayc,as;faeKGacsresrcMnYnsmIkarlMnwgsmmUlsMrab;kar edaHRsay. CaTUeTAeKGacsresrsmIkarlMnwgbIsMrab;Ggát;nImYy² elIkElgGgát;Edl mankMlaMgBIr. dMeNaHRsaysMrab;GBaØatnwgminsμúKsμaj RbsinebIeKGnuvtþsmIkarm:Um:g; ∑ M O = 0 kan; EteRcIn. enAeBlGnuvtþsmIkarkMlaMg ∑ Fx = 0 nig ∑ Fy = 0 eKRtUvbMEbkkMlaMgpÁÜbeGayeTACa bgÁúMkMlaMgtamG½kS x nigG½kS y . RbsinebIdMeNaHRsayénsmIkarlMnwgeGayCaTMhMGviC¢mansMrab;kMlaMg b¤m:Um:g;KUEdlCa GBaØat vabgðajfaTisedArbs;k,alRBYjpÞúyBIGVIEdleyIg)ansnμt;enAelIdüaRkamGgÁesrI. ]TahrN_ 2>7³ kMNt;kMlaMgRbtikmμenAelIFñwmEdlbgðajenAkñúgrUbTI 2-27a. karviPaKrcnasm<½n§kMNt;edaysþaTic T.Chhay -45
23. 23. mhaviTüal½ysMNg;sIuvil viTüasßanCatiBhubec©keTskm<úCa dMeNaHRsay³ düaRkamGgÁesrI³ dUcbgðajenAkñúgrUbTI 2-27b kMlaMg 270kN RtUv)anbMEbkCabgÁúMkMlaMgtamG½kS x nig y . elIsBIenH eKminRtUvkarrgVas;RbEvg 2.1m eT edaysarm:Um:g;KUKμanviucT½r (free vector) ehIyeKGac GnuvtþvaenARKb;TItaMgTaMgGs;rbs;FñwmsMrab;KNnakMlaMgRbtikmμ. smIkarlMnwg³ edayGnuvtþsmIkar 2-2 CabnþbnÞab; edayeRbIlT§plEdlKNnaBIxagelI eyIg)an³ + → ∑ Fx = 0 Ax − 270 cos 60 o = 0 Ax = 135kN / + ∑ M A = 0 − 270 sin 60 o (3) + 270 cos 60 o (0.3) + B y (4.2) − 67.5 = 0 B y = 173.4kN + ↑ ∑ Fy = 0 − 270 sin 60o + 173.4 + Ay = 0 Ay = 60.4kN ]TahrN_ 2>8³ kMNt;kMlaMgRbtikmμenAelIFñwmenAkñúgrUbTI 2-28 a. dMeNaHRsay³ düaRkamGgÁesrI³ dUcbgðajenAkñúgrUbTI 2-28b kMlaMgBRgayragctuekaNBñayRtUv)anbMElgCakMlaMg BRgayragRtIekaN nigBRgayesμI. kMlaMgBRgayragRtIekaN nigBRgayesμIRtUv)ansMEdgCakMlaMgpÁÜb. kMlaMgpÁÜbTaMgenHmanGMeBIkat;tamTIRbCMuTMgn;rbs;RkLaépÞkMlaMgEdlRtUvKña. smIkarlMnwg³ edayGnuvtþsmIkar 2-2 CabnþbnÞab; edayeRbIlT§plEdlKNnaBIxagelI eyIg)an³ + → ∑ Fx = 0 Ax = 0 + ↑ ∑ Fy = 0 Ay − 60 − 60 = 0 Ay = 120kN / + ∑ M A = 0 − 60(4 ) − 60(6 ) + M A = 0 M A = 600kN .m c]TahrN_ 2>9³ kMNt;kMlaMgRbtikmμenAelIFñwmenAkñúgrUbTI 2-29 a. snμt;fa A CaTMrsnøak; ehIy B CaTMrkl; ¬épÞrelag¦. Analysis of Statically Determinate Structures T.Chhay -46
24. 24. Department of Civil Engineering NPIC dMeNaHRsay³ düaRkamGgÁesrI³ dUcbgðajenAkñúgrUbTI 2-29b TMrkl;enARtg;cMnuc B GnuvtþkMlaMgEkgeTAelIFñwmenA Rtg;cMnucEdlvab:H. ExSskmμénkMlaMgTaMgenHRtUv)ankMNt;edayRtIekaN 3-4-5. smIkarlMnwg³ bMEbkkMlaMg N B eGayeTACabgÁúMkMlaMgtamTis x nigtamTis y ehIyedayeFVIpl bUkm:Um:g;Rtg;cMnuc A eyIgnwgTTYl)ankMlaMg N B edaypÞal;. edayeRbIlT§plenH eyIgGacTTYl)an Ax nig Ay . ⎛3⎞ ⎛4⎞ +∑MA = 0 − 15.75(10.5) + N B ⎜ ⎟(3) + N B ⎜ ⎟(1.2) = 0 N B = 6kN ⎝5⎠ ⎝5⎠ + Ax − (6) = 0 4 → ∑ Fx = 0 Ax = 4.8kN 5 Ay − 15.75 + (6 ) = 0 3 + ↑ ∑ Fy = 0 Ay = 12.15kN 5 ]TahrN_ 2>10³ FñwmpSMenAkñúgrUbTI 2-30 a RtUv)anbgáb;enARtg;cMnuc A . kMNt;kMlaMgRbtikmμenA Rtg; A / B nig C . snμt;fa B CatMNsnøak; ehIy C CaTMrkl;. karviPaKrcnasm<½n§kMNt;edaysþaTic T.Chhay -47
25. 25. mhaviTüal½ysMNg;sIuvil viTüasßanCatiBhubec©keTskm<úCa dMeNaHRsay³ düaRkamGgÁesrI³ düaRkamGgÁesrIénkMNat;Ggát;nImYy²RtUv)anbgðajenAkñúgrUbTI 2-30b. ehtuGVIk¾ lMhat;enHCaeRKOgbgÁúMkMNt;edaysþaTic? smIkarlMnwg³ eKmanGBaØatTaMgGs;6. edayGnuvtþsmIkarlMnwgTaMg6 eyIg)an sMrab;kMNat; BC ³ + ∑MC = 0 − 8 + B y (4.5) = 0 B y = 1.78kN + → ∑ Fx = 0 Bx = 0 + ↑ ∑ Fy = 0 − 1.78 + C y = 0 C y = 1.78kN sMrab;kMNat; AB ³ +∑MA = 0 M A − 36(3) + 1.78(6 ) = 0 M A = 97.3kN .m + → ∑ Fx = 0 Ax − 0 = 0 + ↑ ∑ Fy = 0 Ay − 36 + 1.78 = 0 Ay = 34.2kN ]TahrN_ 2>11³ eRKOgbgÁúMEdlbgðajenAkñúgrUb RTkMral nigBüÜrTUk. m:UEDleRKOgbgÁúMEdlbgðaj enAkñúgrUbenHRtUv)anbgðajenAkñúgrUbTI 2-31a EdleyIgsnμt;fa A CaTMrkl; ehIy B CaTMrsnøak;. edayeRbIkUdkñúgtMbn; (local code) bnÞúkkMralEdl snμt;RtUv)aneTAelIr:tKW 6kN / m . xül;Gnuvtþ kMlaMgpÁÜbtamTisedk 4kN dUcbgðaj ehIym:as;rbs;TUkEdlBüÜreTAnwgr:tKW 23Mg . TIRbCMuTMgn;rbs; m:as;TUksßitenARtg; G . kMNt;kMlaMgRbtikmμenARtg;TMr. Analysis of Statically Determinate Structures T.Chhay -48
26. 26. Department of Civil Engineering NPIC dMeNaHRsay³ düaRkamGgÁesrI³ enATIenH eyIgnwgBicarNaTUk nigr:tCaRbB½n§EtmYy ¬rUbTI 2-31b¦. dUcbgðaj eK RtUvdak;bnÞúkpÁÜbCMnYseGaybnÞúkBRgay. smIkarlMnwg³ edayGnuvtþsmIkar 2-2 CabnþbnÞab;. eyIg)an + → ∑ Fx = 0 4 − Bx = 0 + ∑MB = 0 22.8(1.90 ) − Ay (2) + 225.6(5.40) − 4(0.30) = 0 Ay = 630.2kN = 630kN + ↑ ∑ Fy = 0 630.2 − B y − 22.8 − 225.6 = 0 B y = 382kN cMMNaMfa³ RbsinebIeKBicarNar:tEtmYysMrab;karviPaK enaHkMlaMgEkgenARtg;cMnuc C nig D RtUv)anKit dMbUgedayeRbIdüaRkamGgÁesrIénTUk. kMlaMgTaMgenHnwgmanRbsinebIkabTajTUkeGayb:Hp¥wbnwgcMnuc TaMgBIr. kMlaMgEkgEdlmanTMhMesμIKña EtTisenApÞúyKñaenARtg;cMnuc C nwgeFVIGMeBIeTAelIr:t enAeBleK EdleKBicarNadüaRkamGgÁesrIrbs;va. eKnwgTTYl)anlT§pldUcKña. b:uEnþ edayBicarNaRbB½n§TUk nigr:t kMlaMgEkg nigkMlaMgkabkøayeTACakMlaMgkñúg ehIyminRtUv)aneKykmkKiteT. ]TahrN_ 2>12³ kMNt;bgÁúMkMlaMgRbtikmμedk nigQrenARtg;snøak; A / B nig C rbs;eRKagEdlman GgÁt;BIrdUcbgðajenAkñúgrUbTI 2-32a. karviPaKrcnasm<½n§kMNt;edaysþaTic T.Chhay -49
27. 27. mhaviTüal½ysMNg;sIuvil viTüasßanCatiBhubec©keTskm<úCa dMeNaHRsay³ düaRkamGgÁesrI³ düaRkamGgÁesrIénGgát;nImYy²RtUv)anbgðajenAkñúgrUbTI 2-32b. smIkarlMnwg³ edayGnuvtþnUvsmIkarlMnwgcMnYn6 enAkñúgCMhanbnþbnÞab;GnuBaØateGayeyIgTTYl)an dMeNaHRsaysMrab;GBaØatTaMg6edaypÞal;. sMrab;Ggát; BC ³ + ∑MC = 0 − B y (2) + 6(1) = 0 B y = 3kN sMrab;Ggát; AB ³ +∑MA = 0 − 8(2 ) − 3(2 ) + Bx (1.5) = 0 Bx = 14.7kN + → ∑ Fx = 0 Ax + 3 (8) − 14.7 = 0 Ax = 9.87kN 5 Ay − (8) − 3 = 0 4 + ↑ ∑ Fy = 0 Ay = 9.40kN 5 sMrab;Ggát; BC ³ + → ∑ Fx = 0 14.7 − C x = 0 C x = 14.7kN + ↑ ∑ Fy = 0 3 − 6 + Cy = 0 C y = 3kN ]TahrN_ 2>13³ RCugrbs;GKarenAkñúgrUbTI 2-33a rgnUvbnÞúkxül;EdlbegáItCasMBaFEkgBRgay esμI 15kPa enAelICBa¢aMgEdlRbQmnwgTisxül;bk; (windward side) nigrgsMBaFbWt (suction pressure) 5kPa enAelICBa¢aMgEdlminRbQmnwgTisxül;bk; (leeward side). kMNt;bgÁúMkMlaMgRbtikmμ edk nigQrenARtg;snøak; A / B nig C énTMrrbs; gable arch. Analysis of Statically Determinate Structures T.Chhay -50
28. 28. Department of Civil Engineering NPIC dMeNaHRsay³ edaysarbnÞúkCabnÞúkBRgayelIépÞ enaHeKRtUvbMElgbnÞúkenHeGayeTACabnÞúkBRgayelIbnÞat; mann½y fa gable arch kNþalRTnUvbnÞúkEdleFVIGMeBIenAelICBa¢aMg nigdMbUlrbs;épÞrgsMBaFEdlmanBN’dit. bnÞúkBRgayelIenAelIRCugEdlRtUvnwgTisxül;bk;KW (15kN / m 2 )(4m) = 60kN / m ehIyenAelIRCug mYyeTotKW (5kN / m 2 )(4m) = 20kN / m ¬rUbTI 2-33b¦. düaRkamGgÁesrI³ edaysMrYlKitbnÞúkBRgayCabnÞúkpÁÜbcMcMnuc düaRkamGgÁesrIrbs;eRKagTaMgmUl nigrbs;Ggát;nImYy²RtUv)anbgðajenAkñúgrUbTI 2-33c. smIkarlMnwg³ eKRtUveCosvagdMeNaHRsaykñúgeBlEtmYy edayGnuvtþsmIkarlMnwgenAkñúgCMhanbnþbnÞab;dUcbgðajenAkñúg]TahrN_xagelI . * eRKagTaMgmUl³ +∑MA = 0 − (180 + 60 )(1.5) − (254.6 + 84.9 )cos 45o (4.5) − (254.6 sin 45o )(1.5) + (84.9 sin 45o )(4.5) + C y (6) = 0 C y = 240.0kN + ↑ ∑ Fy = 0 − Ay − 254.6 sin 45o + 84.9 sin 45o + 240.0 = 0 Ay = 120.0kN sMrab;Ggát; AB ³ + ∑MB = 0 − Ax (6) + 120.0(3) + 180(4.5) + 254.6(2.12) = 0 Ax = 285.0kN + → ∑ Fx = 0 − 285.0 + 180 + 254.6 cos 45o − Bx = 0 Bx = 75.0kN + ↑ ∑ Fy = 0 − 120.0 − 254.6 sin 45o + B y = 0 B y = 300.0kN sMrab;Ggát; BC ³ + → ∑ Fx = 0 − C x + 60 + 84.9 cos 45o + 75.0 = 0 C x = 195.0kN * eKk¾GacedaHRsay]TahrN_enHedayGnuvtþsmIkarlMnwgEtcMnYn6eTAelIGgát;TaMgBI. RbsinvaGaceTArYc vaCakarRbesIrEdl dMbUleyIgRtUv eFVIplbUkm:Um:gRtg;cMnuc A enAelIGgát; AB bnÞab;mkRtg;cMnuc C enAelIGgát; CB. edayeFVIEbbenH eyIgnwg TTYl)anBIrsmIkarsMrab;edaHRsayrk B nig B kñúgeBlCamYyKña. x y karviPaKrcnasm<½n§kMNt;edaysþaTic T.Chhay -51
29. 29. mhaviTüal½ysMNg;sIuvil viTüasßanCatiBhubec©keTskm<úCa cMeNaT 2>1> eKeRbIeRKagmYyeGayRTkMraleQI ¬min BE nig FD . yk b = 3m / a = 2.4m . CMnYy³ bgðaj¦ EdlvargbnÞúkBRgayesμI 6.5kN / m 2 . emIltarag 1-3. KUrbgðajBIbnÞúkEdlmanGMeBIenAelIGgát; BG nig ABCD . yk b = 3m / a = 1.5m . 2>4> edaHRsaycMeNaT 2-3/ CamYynwg b = 3 .6 m / a = 1 .2 m . 2>2> kMraldMbUlénGKarEdlmankMBs;mYyCan; 2>5> eKeRbIeRKageQIedIm,IRTkMraleQI. bgðaj rgnUvbnÞúkefr nigbnÞúkGefr 6kN / m 2 . Rbsin bnÞúkEdlmanGMeBIelIGgát; BG nig ABCD . yk b = 3m / a = 1.5m . CMnYy³ emIltarag 1-4. ebIrnUtmanKMlatBIKña1.2m ehIyr:tmanKMlat 7.5m BIKña cUrkMNt;bnÞúkBRgayEdleFVIGMeBIelI rnUt DF nigbnÞúkEdleFVIGMeBIelIr:tenARtg;cMnuc A / B / C / D nig E . 2>6> edaHRsaycMeNaT 2-5/ CamYynwg b = 2 .4 m / a = 2 .4 m . 2>7> edaHRsaycMeNaT 2-5/ CamYynwg b = 4.5m / a = 3m . 2>8> cat;cMNat;fñak;éneRKOgbgÁúMnImYy²CaeRKOg bgÁúMkMNt;edaysþaTic eRKOgbgÁúMminkMNt;edaysþa 2>3> eKeRbIeRKagEdkedIm,IRTkMralebtugGarem: Tic eRKOgbgÁúMmansßirPaB b¤eRKOgbgÁúMKμanesßr PaB. TMgn;RsalkMras; 100mm EdlRTbnÞúkBRgayesμI RbsinebICaeRKOgbgÁúMminkMNt;edaysþaTic 25kN / m 2 . bgðajbnÞúkEdlmanGMeBIelIGgát; cUrkMNt;BIdWeRkénPaBminkMNt;. Problems T.Chhay -52
30. 30. Department of Civil Engineering NPIC 2>10> cat;cMNat;fñak;éneRKOgbgÁúMnImYy²Ca eRKOgbgÁúMkMNt;edaysþaTic eRKOgbgÁúMminkMNt; edaysþaTic b¤eRKOgbgÁúMKμansßirPaB. RbsinebICa eRKOg bgÁúMminkMNt;edaysþaTic cUrkMNt;BIdWeRkén PaBminkMNt;. 2>9> cat;cMNat;fñak;éneRKOgbgÁúMnImYy²CaeRKOg bgÁúMkMNt;edaysþaTic eRKOgbgÁúMminkMNt;edaysþa Tic b¤eRKOgbgÁúMKμansßirPaB. RbsinebICaeRKOg bgÁúMminkMNt;edaysþaTic cUrkMNt;BIdWeRkénPaB minkMNt;. 2>11> cat;cMNat;fñak;éneRKOgbgÁúMnImYy²Ca eRKOgbgÁúMkMNt;edaysþaTic eRKOgbgÁúMminkMNt; edaysþaTic b¤eRKOgbgÁúMKμansßirPaB. RbsinebICa eRKOgbgÁúMminkMNt;edaysþaTic cUrkMNt;BIdWeRkén PaBminkMNt;. cMeNaT T.Chhay -53
31. 31. mhaviTüal½ysMNg;sIuvil viTüasßanCatiBhubec©keTskm<úCa edaysþaTic b¤eRKOgbgÁúMKμansßirPaB. RbsinebICa eRKOgbgÁúMminkMNt;edaysþaTic cUrkMNt;BIdWeRkén PaBminkMNt;. TMr nigtMNTaMgGs;RtUv)ansnμt; dUcbgðaj. 2>12> cat;cMNat;fñak;éneRKOgbgÁúMnImYy²Ca eRKOgbgÁúMkMNt;edaysþaTic eRKOgbgÁúMminkMNt; edaysþaTic b¤eRKOgbgÁúMKμansßirPaB. RbsinebICa eRKOgbgÁúMminkMNt;edaysþaTic cUrkMNt;BIdWeRkén PaBminkMNt;. TMr nigsnøak;RtUv)ansnμt;dUc bgðaj. 2>14> cat;cMNat;fñak;éneRKOgbgÁúMnImYy²Ca eRKOgbgÁúMkMNt;edaysþaTic eRKOgbgÁúMminkMNt; edaysþaTic b¤eRKOgbgÁúMKμansßirPaB. RbsinebICa eRKOgbgÁúMminkMNt;edaysþaTic cUrkMNt;BIdWeRkén PaBminkMNt;. tMNTaMgGs;CatMNrwg b¤tMNbgáb;. 2>13> cat;cMNat;fñak;éneRKOgbgÁúMnImYy²Ca eRKOgbgÁúMkMNt;edaysþaTic eRKOgbgÁúMminkMNt; Problems T.Chhay -54
32. 32. Department of Civil Engineering NPIC 2>16> cat;cMNat;fñak;éneRKOgbgÁúMnImYy²Ca eRKOgbgÁúMkMNt;edaysþaTic eRKOgbgÁúMminkMNt; edaysþaTic b¤eRKOgbgÁúMKμansßirPaB. RbsinebICa eRKOgbgÁúMminkMNt;edaysþaTic cUrkMNt;BIdWeRkén PaBminkMNt;. TMr nigtMNTaMgGs;RtUv)ansnμt; 2>15> cUrkMNt;BIdWeRkénPaBminkMNt;rbs; dUcbgðaj. eRKOgbgÁúMminkMNt;edaysþaTic. tMNTaMgGs; CatMNrwg b¤tMNbgáb;. cMeNaT T.Chhay -55
33. 33. mhaviTüal½ysMNg;sIuvil viTüasßanCatiBhubec©keTskm<úCa 2>20> kMNt;kMlaMgRbtikmμenAelIFñwm. 2>21> kMNt;kMlaMgRbtikmμenAelIFñwm. 2>17> kMNt;kMlaMgRbtikmμenAelIFñwm. eKsnμt; TMrenARtg; B CaTMrkl; nigminKitBIkMras;rbs;Fñwm. 2>22> kMNt;kMlaMgRbtikmμenARtg;TMr A nig B . kMral CD / DE / EF nig FG bBa¢ÚnbnÞúkrbs;va eTAelIr:ttamTMrkl;. snμt; A CaTMrkl; nig B CaTMrsnøak;. 2>18> kMNt;kMlaMgRbtikmμenARtg;TMr A nig B . snμt; A CaTMrkl; nig B CaTMrsnøak;. 2>23> KNnakMlaMgRbtikmμenARtg;TMr A nig B énFñwmpSM. enARtg; C CatMNsnøak;. 2>19> kMNt;kMlaMgRbtikmμenAelIFñwm. Problems T.Chhay -56
34. 34. Department of Civil Engineering NPIC 2>24> eKeRbIRKwHeCIgtagedIm,IRTbnÞú 50kN . kM- Nt;GaMgtg;sIuet w1 nig w2 énbnÞúkBRgayEdl manGMeBIenAelI)atrbs;RKWHedIm,IeGaymanlMnwg. 2>28> eKeRbIeCIgtagkugs‘ul (cantilever footing) edIm,IRTCBa¢aMgenAEk,rcugEKmrbs;RKwH A dUcenH vaeFVIeGaymansMBaFdIrayesμIenABI eRkamRKwH. kMNt;bnÞúkBRgayesμIcaM)ac; wA nig wB EdlKitCa kN / m enARtg;RKwH A nig B edIm,I 2>25> kMNt;kMlaMgRbtikmμenAelIFñwm. RTbnÞúkCBa¢aMg 40kN nig100kN . 2>26> KNnakMlaMgRbtikmμenARtg;TMrrelag C nigenARtg;TMrsnøak; A . snμt; B CatMNbgáb; . 2>29> kMNt;kMlaMgRbtikmμenARtg;TMr A nig B rbs; truss. bnÞúkBRgayRtUv)anbgáeLIgeday sarxül;. 2>27> KNnakMlaMgRbtikmμenARtg;TMrrelag A nigenARtg;TMrsnøak; B . tMN C CatMNbgáb; . cMeNaT T.Chhay -57
35. 35. mhaviTüal½ysMNg;sIuvil viTüasßanCatiBhubec©keTskm<úCa 2>30> dgsÞÚc jib crane mantMNsnøak;enARtg; A nigmanTMr smooth collar enARtg; B . kMNt; bMlas;TI x énbnÞúk 22.5kN dUcenHvaeFVIeGayman kMlaMgRbtikmμGtibrma nigGb,brma. KNnakM- laMgRbtikmμenAkñúgkrNInImYy². snμt;eKecal TMgn;rbs;dgsÞúc. eKtMrUveGay1.2m ≤ x ≤ 3m . 2>33> kMNt;bgÁúMkMlaMgRbtikmμedk nigQrenA Rtg;TMr A nig B . tMNenARtg; C nig D CatMN bgáb; . 2>31> kMNt;kMlaMgRbtikmμenARtg;TMr A nig B 2>34> kMNt;kMlaMgRbtikmμenARtg;TMr A / B nig éneRKag. snμt;fa A CaTMrkl;. E . snμt; B CaTMrkl;. 2>35> kMNt;kMlaMgRbtikmμenARtg;TMr A / B / C nig D . 2>32> kMNt;kMlaMgRbtikmμenARtg;TMr A nig B rbs; truss. bnÞúkBRgayRtUv)anbgáeLIgeday sarxül;. Problems T.Chhay -58
36. 36. Department of Civil Engineering NPIC 2>36> kMNt;kMlaMgRbtikmμenRtg;TMrsMrab;FñwmpSM. eKmansnøak;enARtg; A / E nig F . 2>37> sMNg;s<anRtUv)anbgðajenAkñúgrUb. enATI enHeyIgeXIjfa truss kNþal CD RtUv)anRT 2>40> kMNt;kMlaMgRbtikmμenARtg; A / B . snμt; eday truss ly ABC nig DEF . C nig D B CaTMrkl; ¬TMrrGil¦ C CatMNrwg. CatMNsnøak;. kMNt;RbtikmμbBaÄrenARtg;TMr A / B / E nig F RbsinebIbnÞúk 60kN manGMeBIenA elI truss kNþal. 2>38> kMNt;kMlaMgRbtikmμenARtg;TMr A / C nig D. 2>41> kMNt;kMlaMgRbtikmμenARtg;TMr A nig B . 2>42> eRKags<anmYypSMeLIgedaybIkMNat; Edl 2>39> kMNt;kMlaMgRbtikmμenARtg; A nig C . eKKitfa A / D nig E Casnøak; ehIy C nig F snμt;fa A CaTMrkl; B CatMNbgáb; nig C Ca CaTMr rocker É B CaTMrkl;. kMNt;bgÁúMkMlaMgRbti tMNsnøak;. kmμtamTisedk nigTisQrenARKb;TMrTaMgGs; EdlbNþalBIbnÞúkEdl)anbgðaj. cMeNaT T.Chhay -59
37. 37. mhaviTüal½ysMNg;sIuvil viTüasßanCatiBhubec©keTskm<úCa 2>43> kMNt;bgÁúMkMlaMgRbtikmμedk nigQrenA Rtg; A / B nig C . snμt;eKP¢ab;eRKagedaytMN snøak;enARtg;cMnucTaMgenH ehIy D nig E CatMN 2>46> kMNt;kMlaMgRbtikmμenARtg;TMr A nig D . rwg. snμt;fa A CaTMrbgáb; ehIy B / C nig D Casnøak;. 2>44> kMNt;kMlaMgRbtikmμenARtg;TMr A nig B . tMN C nig D CatMNrwg. 2>47> kMNt;kMlaMgRbtikmμenARtg;TMr A nig C . eRKagRtUv)antP¢ab;edaytMNsnøak;enARtg; A / B nig C ehIytMNTaMgBIrCaTMrrwg. 2>45> kMNt;bgÁúMkMlaMgRbtikmμedk nigQrenA Rtg;TMr A nig B . Problems T.Chhay -60
38. 38. Department of Civil Engineering NPIC 2>48> kMNt;kMlaMgRbtikmμenARtg;tMN A / B nig C . snμt;tMNnImYy²CatMNsnøak; ehIytMN B CatMNrwg. KMerag³ pøÚvrfePøIgRtUv)anRTedayeRKagebtug Garem:. snμt;r:tTMrsmBaØBIrRTEdk rail nigkMral pøÚvrfePøIgEdlmanTMgn; 7.5kN / m nigRTbnÞúk rbs;rfePøIg 100kN / m ¬rUbxageRkam¦. r:t nImYy²manRbEvg 100kN / m . GnuvtþbnÞúkTaMg 2>49> kMNt;bgÁúMkMlaMgRbtikmμenARtg;tMN A nig enHeTAelIeRKags<anTaMgmUl ehIykMNt;kMlaMg C én gable frame. snμt;fa A / B nig C Ca sgát;enAkñúgssrrbs;va. sMrab;karviPaKsnμt;fa tMNsnøak;. eKdak;bnÞúkenARtg;cMnuc D / E / F tMNTaMgGs;CatMNsnøak; ehIyecalTMrg;rbs; nig G EkgeTAnwgG½kSrbs;r:tnImYy². eRKag. etIkarsnμt;tMNTaMgGs;CatMNsnøak;Gac TTYlyk)aneTsMrab;PaBCak;Esþg? 2>50> kMNt;bgÁúMkMlaMgRbtikmμedk nigQrenA Rtg;TMr A / B nig C . snμt;faeRKagRtUv)antP¢ab; edaytMNsnøak;enARtg; A / B / D / E nig F É C CaTMrbgáb;. cMeNaT T.Chhay -61